Drafts by Christopher Arnold

Classical general relativity predicts that black holes contain spacetime singularities, where cur... more Classical general relativity predicts that black holes contain spacetime singularities, where curvature invariants diverge and the theory breaks down. We show that within the conformal-entropy gravity framework, such divergences are eliminated. In this approach, the physical metric is conformally related to an auxiliary metric, with the conformal factor determined by a renormalized local entanglement entropy density. Quantum field theory bounds ensure that this entropy density saturates at a finite maximum. When saturation occurs, the conformal factor becomes constant, derivative terms vanish in the curvature relations, and the auxiliary geometry obeys ordinary Einstein equations with finite sources. Consequently, all curvature invariants remain finite: the black hole interior is not singular, but an entropy-saturated finite-curvature core. We provide explicit derivations from the action principle, analyze the consistency of the construction, and address potential objections. Finally, we identify observational consequences: late-time gravitational-wave echoes from black hole mergers and small shifts in the photon ring observed in black hole shadows. These signatures offer near-and mid-term tests of the framework with current and forthcoming instruments.

We extend the anomaly-matched entropic-conformal framework, previously developed for gravity, to ... more We extend the anomaly-matched entropic-conformal framework, previously developed for gravity, to incorporate the SU (2)L × U (1)Y electroweak sector. In place of the explicit Higgs mass parameter of the Standard Model, we introduce a Weyl-covariant potential V (H, Ω) = λ H † H-αΩ 2 2 , where the conformal factor Ω(x) is fixed by the renormalized entanglement entropy density Sent(x) through the anomaly-matching relation Ω 2 = β⋆Sent(x). Electroweak symmetry breaking then occurs dynamically, with the Higgs vacuum expectation value given by v(x) = √ 2α Ω(x). All gauge boson and fermion masses scale proportionally with Ω(x), so that in the adiabatic limit ∇Ω ≈ 0 the theory reduces exactly to the Standard Model. Quantum consistency is maintained: the SM field content contributes to the same anomaly coefficients (a, c) that determine β⋆, while gauge anomalies cancel as usual. Phenomenological deviations appear only through gradients of Ω, generating derivative couplings suppressed by the adiabaticity parameter εΩ. These are consistent with collider data, equivalence-principle tests, astrophysical observations, and cosmological bounds. Unlike Coleman-Weinberg, dilaton Higgs, or technicolor models, this embedding eliminates explicit scales without introducing new propagating fields or strong sectors. We conclude that both gravitational and electroweak scales originate from the same anomaly-driven conformal factor, providing a unified, information-theoretic explanation for the emergence of fundamental scales in nature.
We extend the entropic conformal framework in which the physical metric gµν is conformal to an au... more We extend the entropic conformal framework in which the physical metric gµν is conformal to an auxiliary metric ĝµν with conformal factor fixed by renormalized small-ball entanglement entropy, Ω 2 (x) = β⋆Sent(x). Promoting Ω = e τ to a Weyl compensator and spurionizing the QCD couplings so that the local renormalization scale is µe-τ (x) yields a gauge action SYM[A; τ, ĝ] =-1 4 d 4 x-ĝ Z(µe-τ (x)) ĝµρ ĝνσ F a µν F a ρσ ,

We propose and develop a framework in which the electromagnetic properties of the vacuum are not ... more We propose and develop a framework in which the electromagnetic properties of the vacuum are not fundamental constants, but emergent functions of quantum entanglement entropy. Using the renormalized smallball limit of entanglement entropy as a bona fide local scalar, we introduce a constitutive function χ(Sent) multiplying the Maxwell kinetic term. Replica trick and modular Hamiltonian arguments fix the susceptibility of Sent to coupling variations, while local renormalization group analysis and QED anomaly coefficients determine the flow equation for χ. To leading order, this yields an exponential law χ(S) = χ0 exp[-κ(S-S0)] with slope κ proportional to the QED beta function. Variations in the finestructure constant then follow the linear relation ∆α/α ≃ κ ∆Sent. We derive the modified field equations, stress-energy tensor, and boundary terms explicitly, showing that gauge invariance, current conservation, and Weyl invariance are preserved. Worked examples in thermal states and near-horizon Rindler regimes demonstrate how entanglement gradients induce controlled variations in α. Phenomenological translation yields direct bounds on ∆Sent from atomic clocks, cavity QED, quasar absorption spectra, and Oklo data, while allowing substantial local gradients in extreme environments consistent with global homogeneity. This construction embeds electromagnetism into the broader conformal-entropic paradigm previously applied to gravity, suggesting a unifying principle: that both geometry and gauge response are determined by quantum entanglement, with anomaly coefficients providing the bridge between microphysics and effective constants of nature.

We show that if the physical metric gµν is conformal to an auxiliary metric ĝµν with conformal fa... more We show that if the physical metric gµν is conformal to an auxiliary metric ĝµν with conformal factor fixed by a local, renormalized smallball entanglement-entropy density Sent(x) via Ω 2 (x) = β⋆Sent(x), then varying a covariant action with a Lagrange constraint yields Einstein's equations exactly when the conformal factor is constant-equivalently when β⋆Sent is constant-and a specific, Bianchi-compatible modification when Ω varies. We define Sent(x) from the replica/OPE expansion, isolating its universal term s0(x) in a controlled semiclassical regime ℓ Pl ≪ ℓ ≪ min{Lcurv, L mfp }. We derive the conformal transformation of curvature tensors used in the action and verify preservation of the contracted Bianchi identity. The anomaly-matched coefficient β⋆ is fixed up to known QFT Weyl-anomaly coefficients, ensuring GR recovery in the limit β⋆ → 0. As a conservative demonstration, we apply the weak-field limit to one well-characterized galaxy as a parameter-consistency check; we do not claim to resolve dark matter, singularities, or gravitational-wave echoes here. The paper's contribution is a precise field-theory definition of Sent, a conservative covariant action principle, and a worked derivation that recovers GR while yielding a falsifiable one-parameter extension.
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Drafts by Christopher Arnold